Breakdown, filler cluster

Backbone fractal dimension 54 Bending-twisting deformation 55 BET-surface area 13-14, 20 Brake system, frictional 145 Breakdown, filler cluster 64, 76... 

For a consideration of filler-network breakdown at increasing strain, the failure properties of filler-filler bonds and filler clusters have to be evaluated in dependence of cluster size. This allows for a micromechanical description of tender but fragile filler clusters in the stress field of a strained mbber matrix. A schematic view of the mechanical equivalence between a CCA-filler cluster and a series of soft and hard springs is presented in Figure 22.9. The two springs with force constants... 

In particular it can be shown that the dynamic flocculation model of stress softening and hysteresis fulfils a plausibility criterion, important, e.g., for finite element (FE) apphcations. Accordingly, any deformation mode can be predicted based solely on uniaxial stress-strain measurements, which can be carried out relatively easily. From the simulations of stress-strain cycles at medium and large strain it can be concluded that the model of cluster breakdown and reaggregation for prestrained samples represents a fundamental micromechanical basis for the description of nonlinear viscoelasticity of filler-reinforced rubbers. Thereby, the mechanisms of energy storage and dissipation are traced back to the elastic response of tender but fragile filler clusters [24]. 

So far, we have considered the elasticity of filler networks in elastomers and its reinforcing action at small strain amplitudes, where no fracture of filler-filler bonds appears. With increasing strain, a successive breakdown of the filler network takes place and the elastic modulus decreases rapidly if a critical strain amplitude is exceeded (Fig. 42). For a theoretical description of this behavior, the ultimate properties and fracture mechanics of CCA-filler clusters in elastomers have to be evaluated. This will be a basic tool for a quantitative understanding of stress softening phenomena and the role of fillers in internal friction of reinforced rubbers. 

Cyclic breakdown and re-aggregation of the residual fraction of fragile, soft filler clusters with weaker filler-filler bonds. 

Beside the consideration of the up-cycles in the stretching direction, the model can also describe the down-cycles in the backwards direction. This is depicted in Fig. 47a,b for the case of the S-SBR sample filled with 60 phr N 220. Figure 47a shows an adaptation of the stress-strain curves in the stretching direction with the log-normal cluster size distribution Eq. (55). The depicted down-cycles are simulations obtained by Eq. (49) with the fit parameters from the up-cycles. The difference between up- and down-cycles quantifies the dissipated energy per cycle due to the cyclic breakdown and re-aggregation of filler clusters. The obtained microscopic material parameters for the viscoelastic response of the samples in the quasi-static limit are summarized in Table 4. 

In view of an illustration of the viscoelastic characteristics of the developed model, simulations of uniaxial stress-strain cycles in the small strain regime have been performed for various pre-strains, as depicted in Fig. 47b. Thereby, the material parameters obtained from the adaptation in Fig. 47a (Table 4, sample type C60) have been used. The dashed lines represent the polymer contributions, which include the pre-strain dependent hydrodynamic amplification of the polymer matrix. It becomes clear that in the small and medium strain regime a pronounced filler-induced hysteresis is predicted, due to the cyclic breakdown and re-aggregation of filler clusters. It can considered to be the main mechanism of energy dissipation of filler reinforced rubbers that appears even in the quasi-static limit. In addition, stress softening is present, also at small strains. It leads to the characteristic decline of the polymer contributions with rising pre-strain (dashed lines in... 

Even dynamic measurements have been made on mixtures of carbon black with decane and liquid paraffin [22], carbon black suspensions in ethylene vinylacetate copolymers [23], or on clay/water systems [24,25]. The corresponding results show that the storage modulus decreases with dynamic amplitude in a manner similar to that of conventional rubber (e.g., NR/carbon blacks). This demonstrates the existence and properties of physical carbon black structures in the absence of rubber. Further, these results indicate that structure effects of the filler determine the Payne-effect primarily. The elastomer seems to act merely as a dispersing medium that influences the magnitude of agglomeration and distribution of filler, but does not have visible influence on the overall characteristics of three-dimensional filler networks or filler clusters, respectively. The elastomer matrix allows the filler structure to reform after breakdown with increasing strain amplitude. 

The dynamic flocculation model of stress softening and filler induced hysteresis assumes that the breakdown of filler clusters during the first deformation of the virgin samples is totally reversible, though the initial virgin state of filler-... 

The effect of carbon black on hysteresis depends primarily on the particle size of the filler and is related to breakdown and reformation of the agglomerations and the network, to slippage of polymer chains around the periphery of the filler clusters and the presence of occluded rubber. Figure 13 shows the difference of the temperature profiles of carbon black and silica filled rubber compoimds. 

The application of this normalized, relative stress in Eq. (32) is essential for a constitutive formulation of cyclic cluster breakdown and re-aggregation during stress-strain cycles. It implies that the clusters are stretched in spatial directions with deu/dt>0, only, since AjII>0 holds due to the norm in Eq. (33). In the compression directions with ds /dt<0 re-aggregation of the filler particles takes place and the clusters are not deformed. An analytical model for the large strain non-linear behavior of the nominal stress oRjU(eu) of the rubber matrix will be considered in the next section. 

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